ANALYTIC EXPRESSIONS FOR MODE CONVERSION IN A PLASMA WITH A PARABOLICDENSITY PROFILE - GENERALIZED RESULTS

This study provides an analytic solution to the general problem of mod e conversion in an unmagnetized plasma. Specifically, an electromagnet ic wave of frequency omega propagating through a plasma with a parabol ic density profile of scale length L(p) is examined. The mode conversi on points are located a distance DELTA0 from the peak of the profile, where the electron plasma frequency omega(p)(z) matches the wave frequ ency omega. The corresponding reflection, transmission, and mode conve rsion coefficients are expressed analytically in terms of parabolic cy linder functions for all values of DELTA0. The method of solution is b ased on a source approximation technique that is valid when the electr omagnetic and electrostatic scale lengths are well separated. For larg e DELTA0, i.e., (cL(p)/omega)1/2 much less than DELTA0 < L(p), the app ropriately scaled result [D. E. Hinkel-Lipsker et al, Phys. Fluids B 4 , 559 (1992)] for a linear density profile is recovered as the parabol ic cylinder functions asymptotically become Airy functions. When DELTA 0-->0, the special case of conversion at the peak of the profile [D. E . Hinkel-Lipsker et al., Phys. Fluids B 4, 1772 (1992)] is obtained.